The derivation of a closed-form expression is presented for a three-timescale approximation of the point-kinetics equations with two effective groups of delayed neutrons. The results produced by this three-scale approximation are shown to be practically as accurate as the numerical results produced by the Kaganove-type algorithms used in production codes, yet at significantly less cost in computational time and resources. Potential uses of this approximation for increasing the efficiency of production codes for computing the space-time distribution of neutrons in reactors are also indicated.